1. Field of the Invention
The invention relates to the correction of errors in achieving required states as determined by a controller, such as, for example, an autopilot.
In particular, the invention relates to the correction of errors due to an unknown disturbance of non-zero mean.
2. Discussion of Prior Art
When a system is subjected to an unknown constant disturbance, the variables which the state of the system (state variables) cannot, in general, be brought to desired values (the ordered state) by an automatic controller whose inputs consist solely of the differences between the actual and the ordered state (the state errors). The inclusions of derivatives of the state variables does not remedy matters.
Herein, the term "desired state" or "desired value" is used to denote the values desired by the operator, or by an automatic system controlling the operation of an autopilot. The term "ordered state" is used to denote the input settings of the autopilot, by which the desired values are input to the autopilot.
This controller problem can be illustrated by the following examples:
a) A controller depending on inputs of the depth error, pitch angle and their derivatives cannot bring a submarine to ordered depth if the submarine is out of trim (due to, for example, external loads, incorrect ballast or hydroplane offsets). The addition of heave velocity and pitch rate terms is unable to remedy the problem; PA1 b) A similar controller whose input is course error cannot bring ships or submarines to their ordered course when they are subjected to, for example, wind or steering offsets. The addition of sway velocity and yaw rate terms does not remedy the problem; PA1 c) Similarly to (b), ordered track cannot be achieved by a controller of this type whose inputs are distance off track and course error. In the same way as in (b), the addition of sway velocity and yaw rate terms cannot remedy this problem. PA1 1. Pressure fluctuation proportional to wave height are picked up by the depth sensors, causing futile flapping of the hydroplanes, which causes excessive wear and noise; PA1 2. Oscillatory forces cause the submarine to surge, heave and pitch. These do not affect the means depth, and the control system must ignore them since they are too large to be opposed; PA1 3. A second-order force, commonly referred to as `suction force`, acts in an upwards direction only. It has a non-zero mean which must be opposed by the control system. PA1 a) means to provide control inputs to control one or more state variables of a system; PA1 b) means to provide a model of the system; PA1 c) means to estimate from the model of the system the values of the one or more state variables which are expected to occur in response to the control inputs; PA1 d) means to set the desired values of the or each controlled state variable; and PA1 e) means to provide measurement of the or each controlled state variable; PA1 f) means to compare the estimated values of state variables with their measured values by subtracting the estimated values from their corresponding measured values to give the estimation error values; PA1 g) means to derive from the estimation error values the necessary correction to the control means to achieve the desired values, the estimation error values bypassing the model means prior to the control means; and PA1 h) means to adjust the control inputs to produce the desired values of the or each state variable. PA1 1) inputting desired values of one or more state variables of a system into an autopilot controller in the form of ordered states; PA1 2) providing control inputs to the system from the controller to achieve the states corresponding to the ordered states; PA1 3) providing measurement of the actual values of the state variable of the system; and PA1 4) modelling the system in a state estimator; PA1 5) comparing the measured values of the state variables with the values estimated by the state estimator; PA1 6) deriving an error signal by subtracting the estimated values from their corresponding measured values to give the error signal; and PA1 7) using the error signal to provide a correction to the control inputs, the error signal bypassing the state estimator prior to providing correction to the control inputs, which brings the actual states closer to the ordered states.
The control outputs of these controllers are proportional to the state variables, and their derivatives. Hence they are called Proporational Derivative (PD) controllers. PD controllers are simple controllers and are commonly fitted to ships and submarines. In a submarine, for example, the hydroplane deflection is proportional to terms in the depth error (i.e. actual depth-ordered depth) and pitch angel, and their derivatives. Under a constant disturbing force. e.g. out of trim, the controller maintains a constant, but inaccurate depth.
The shortcomings of a PD controller become serious when accurate achievement of a particular ordered state is important, such as when accurate navigation or depth keeping is needed. The addition of a term which is the integral of the appropriate state error variable, as in a Proporational Integral Derivative (PID) controller, can overcome the problem. However, though this can remove the steady state error, it reduces the stability of the system and serious difficulties arise when a change is made in the ordered state. A change in the ordered state creates a step in the corresponding state error variable. Left to itself, the integrator will integrate the error throughout the transition and can only correct itself by a massive overshoot. This can be mitigated by freezing or resetting the integrator, but the problem reappears when the integrator has to be released. There is, as well, the problem of how and when the integrator is to be switched out and reintroduced. Situations will always be possible in which highly undesirable side effects can occur, such as massive overshoot or the integrator not switching back in at all. These shortcomings of the PID controller become serious when, for example, a submarine wishes to ascent to a particular depth, e.g. periscope depth, with no or minimal overshoot.
In any of the systems described above, as an alternative to the integrator, the steady state error could be corrected manually by observing the error and adjusting the ordered state accordingly. This technique requires the steady state to be achieved and observed before the correction can be made. It cannot be applied during a manoeuvre, and it has to be repeated whenever the disturbing force changes. For example, the correction cannot be ascertained during a submarine's depth change. The direct automatic implementation of this technique (by automatically applying the steady state error in the opposite sense to the ordered value) fails, because success requires the error to be removed, and the necessary correction signal thereby vanished also. A successful implementation would require an integrator, or something like it, the disadvantages of which have been described above.
Another manual procedure, similar to that described in the preceding paragraph, uses the steady state errors to calculate offsets which are applied to the controls. This technique is open to the same objections and cannot be implemented automatically.
Everything that has been stated about a constant disturbance applies also to a varying disturbance with a non-zero mean, including a mean which is varying slowly compared with the response of the system. The objective is to bring the means state to the ordered state.
Waves constitute a varying disturbance to a submarine. They affect the system in three ways:
All three effects increase rapidly as the surface is approached. The ascent of a submarine to periscope depth therefore presents a particularly difficult problem. It must be achieved with minimal overshoot by a manoeuvre during which wave effects, which have an unknown but non-zero mean, are increasing.
Modern autopilots minimise the effects of the higher frequencies of the disturbances. They compute the most probable values of all the state variables (for a submarine there include the heave velocity, pitch rate, pitch angle and depth) from measurements that may be noisy. This is done by a state estimator, which models the system. Its output, when subject to the same controls inputs (for example, the hydroplane deflections), is compared with those actually occurring. Ideally, the estimation errors (observed state--estimated state) should be zero. (There is a distinction between the estimation errors, the state errors ie actual-ordered, and the estimated state errors ie estimated-ordered). In practice there are discrepancies due, for example, to the wave effects. By feeding back the estimation errors (those that can be measured), to the model via a Kalman filter, the estimates can be improved. The controller is similar to the PD controller. It includes terms proportional to the estimated state errors. This type of autopilot, possibly with additional filtering, achieves better performance against disturbances at the higher frequencies such as wave frequencies, but it offers no improvement against a constant or non-zero means disturbance. An integrator can be included but with the same disadvantages a the PID.
To summarise, the problem is to bring the mean state to the ordered state in a way which overcomes the difficulties of changing the ordered state. It is common to all autopilots and to many other controlled systems. It cannot be dealt with by presently available systems.